Problem: Solve for $x$ and $y$ using elimination. ${3x+2y = 35}$ ${4x-2y = 28}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $7x = 63$ $\dfrac{7x}{{7}} = \dfrac{63}{{7}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {3x+2y = 35}\thinspace$ to find $y$ ${3}{(9)}{ + 2y = 35}$ $27+2y = 35$ $27{-27} + 2y = 35{-27}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 9}$ into $\thinspace {4x-2y = 28}\thinspace$ and get the same answer for $y$ : ${4}{(9)}{ - 2y = 28}$ ${y = 4}$